To understand how the bottom triode is working as a cathode follower, imagine a voltage pulse applied to the output transformer's secondary. This pulse would reflect back into the primary, forcing the top triode's cathode up and the bottom triode's plate down. And since the top tube's grid is referenced to ground, its cathode moving more positive will decrease this tube's conduction. Likewise, the bottom triode's plate's downward movement will be relayed by the inter-stage transformer's secondary, forcing its grid more negative, decreasing its conduction as well. And a negative going pulse would force the output tubes to conduct more. The lower distortion results from the correction of any voltage across the primary not matching the signal across the grids, as any variation from the grid signal provokes the triodes to compensate (by either increasing or decreasing conduction). The lower output impedance results from the triode's rp being reduced by the mu of the tubes. In other words, the output tubes, configured as cathode followers, buck any extraneous voltages on the output, providing a lower distortion and output impedance as a result.
Because of the cathode follower's slightly less than unity gain, we will need to see about 280 volts of peak-to-peak signal across the inter-stage transformer's secondaries to drive the 2A3 to full output. This is a lot of gain, too much for an inter-stage transformer with a low winding ratio. The driver tube must realize a gain, in this example, equal to the 140 divided by the inter-stage transformer's winding ratio. Thus, if the ratio is 1:10, then a gain of 14 is needed. A 300B will require about twice this amount and an 845 will require about five times more gain. Couldn't a much larger winding ratio be used? In general, fear high winding ratios. The higher the winding ratio, the less likely that the secondary's waveform will match the primary's. (I once picked up a nicely built transformer at a surplus store. I assumed it was just a power transformer. But after hooked it up to a signal generator and scope, I was shocked to see perfect square waves at 10 kHz; its winding ratio was 1:1.4.)